6 002 CIRCUITS AND ELECTRONICS Small Signal Circuits Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Review Small signal notation vA VA va total operating point small signal vOUT f vI d vout f vI vi dv I v I VI VS vI VI vi vi VI RL vO VO vo Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Review I Graphical view using transfer function vO behaves linear for small perturbations vI Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Review II Mathematical view K vI VT vO VS RL 2 2 V K v V 2 R I T L S d 2 vo dvI vi v I VI vo K VI VT RL vi gm related to VI constant for fixed DC bias Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 How to choose the bias point using yet another graphical view based on the load line i DS i DS Demo K 2 vO 2 V S vO i load line DS R R L L input signal response VI VO 1 1 2 KR LV S v I VT KR L vO v I VT Choosing a bias point 1 Gain g m RL VI 2 Input valid operating range for amp 3 Bias to select gain and input swing Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 III The Small Signal Circuit View We can derive small circuit equivalent models for our devices and thereby conduct small signal analysis directly on circuits e g large signal circuit model for amp vI R VS vOUT K 2 iD vI VT 2 1 We can replace large signal models with small signal circuit models Foundations Section 8 2 1 and also in the last slide in this lecture Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Small Signal Circuit Analysis 1 Find operating point using DC bias inputs using large signal model 2 Develop small signal linearized models for elements 3 Replace original elements with small signal models Analyze resulting linearized circuit Key Can use superposition and other linear circuit tools with linearized circuit Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Small Signal Models A MOSFET large signal D vGS Small signal iDS K vGS VT 2 2 S Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Small Signal Models A MOSFET large signal D vGS iDS Small signal K 2 iDS vGS VT 2 ids vGS K 2 vGS VT 2 S K v V 2 v gs T 2 GS vGS VGS ids K VGS VT v gs ids is linear in vgs gm D small signal v gs ids K VGS VT v gs S ids g m v gs Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 B DC Supply VS large signal vS VS iS vS VS Small signal VS vs iS is vs is iS I S vs 0 DC source behaves as short to small signals Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 C Similarly R large signal iR vR R v R R iR vr RiR ir iR iR I R vr R ir small signal ir vr R Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 Amplifier example Large signal RL vO v I iDS Small signal RL vo V S vi iDS K 2 vI VT 2 ids ids K VI VT vi K 2 vO VS vI VT RL 2 ids RL vo 0 vo ids RL vo K VI VT RL vi g m RL vi Notice first we need to find operating point voltages currents Get these from a large signal analysis Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11 III The Small Signal Circuit View To find the relationship between the small signal parameters of a circuit we can replace large signal device models with corresponding small signal device models and then analyze the resulting small signal circuit Foundations Also see section 8 2 1 of A L KVL KCL applied to some circuit C yields v A vOUT vB 1 Replace total variables with operating point variables plus small signal variables VA v a VOUT vout VB vb Operating point variables themselves satisfy the same KVL KCL equations VA VOUT VB so we can cancel them out Leaving va vout vb 2 But 2 is the same equation as 1 with small signal variables replacing total variables so 2 must reflect same topology as in C except that small signal models are used Since small signal models are linear our linear tools will now apply Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 11
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